The multi-body dynamic model of telescopic landing gear with two wheels is established to study the low-frequency brake-induced multi-degree-of-freedom coupled vibration. Parameter study regarding landing gear structure and braking torque is conducted. The results indicate that the strut stiffness of landing gear and the amplitude of braking torque have a significant effect on coupled vibration. When the longitudinal strut stiffness reduces by 30%，the longitudinal acceleration of landing gear increases by more than 60%. When the braking moments on the left and right wheels are the same，30% amplitude of braking moment increases leads to 50% increases of the longitudinal acceleration. In the case of asymmetric braking，the landing gear will have multi-degree-of-freedom coupled vibration. When the difference in braking moments amplitude between two wheels increases from 20% to 40%，the lateral and torsional amplitude，acceleration and load will increase by more than 90%.